| dc.description.abstract | The estimation of conditional quantiles has become an increasingly important issue in
insurance and financial risk management. The stylized facts of financial time series data
has rendered direct applications of extreme value theory methodologies, in the estimation
of extreme conditional quantiles, inappropriate. On the other hand, quantile regression
based procedures work well in nonextreme parts of a given data but breaks down in
extreme probability levels. In order to solve this problem, we combine nonparametric
regressions for time series and extreme value theory approaches in the estimation of extreme conditional quantiles for financial time series. To do so, a class of time series models
that is similar to nonparametric AR-(G)ARCH models but which does not depend on distributional and moments assumptions, is introduced. We discuss estimation procedures
for the nonextreme levels using the models and consider the estimates obtained by inverting conditional distribution estimators and by direct estimation using Koenker-Basset
(1978) version for kernels. Under some regularity conditions, the asymptotic normality
and uniform convergence, with rates, of the conditional quantile estimator for α-mixing
time series, are established. We study the estimation of scale function in the introduced
models using similar procedures and show that under some regularity conditions, the scale
estimate is weakly consistent and asymptotically normal. The application of introduced
models in the estimation of extreme conditional quantiles is achieved by augmenting them
with methods in extreme value theory. It is shown that the overal extreme conditional
quantiles estimator is consistent. A Monte Carlo study is carried out to illustrate the
good performance of the estimates and real data are used to demonstrate the estimation
of Value-at-Risk and conditional expected shortfall in financial risk management and their
multiperiod predictions discussed. | en_US |
